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Simplifying x4 + -6x2 = 5 Reorder the terms: -6x2 + x4 = 5 Solving -6x2 + x4 = 5 Solving for variable 'x'. Reorder the terms: -5 + -6x2 + x4 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + -6x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + -6x2 + 5 + x4 = 0 + 5 Reorder the terms: -5 + 5 + -6x2 + x4 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -6x2 + x4 = 0 + 5 -6x2 + x4 = 0 + 5 Combine like terms: 0 + 5 = 5 -6x2 + x4 = 5 The x term is -6x2. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x2 + 9 + x4 = 5 + 9 Reorder the terms: 9 + -6x2 + x4 = 5 + 9 Combine like terms: 5 + 9 = 14 9 + -6x2 + x4 = 14 Factor a perfect square on the left side: (x2 + -3)(x2 + -3) = 14 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting (x2 + -3) equal to 3.741657387 and -3.741657387.Subproblem 1
x2 + -3 = 3.741657387 Simplifying x2 + -3 = 3.741657387 Reorder the terms: -3 + x2 = 3.741657387 Solving -3 + x2 = 3.741657387 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x2 = 3.741657387 + 3 Combine like terms: -3 + 3 = 0 0 + x2 = 3.741657387 + 3 x2 = 3.741657387 + 3 Combine like terms: 3.741657387 + 3 = 6.741657387 x2 = 6.741657387 Simplifying x2 = 6.741657387 Take the square root of each side: x = {-2.596470178, 2.596470178}Subproblem 2
x2 + -3 = -3.741657387 Simplifying x2 + -3 = -3.741657387 Reorder the terms: -3 + x2 = -3.741657387 Solving -3 + x2 = -3.741657387 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x2 = -3.741657387 + 3 Combine like terms: -3 + 3 = 0 0 + x2 = -3.741657387 + 3 x2 = -3.741657387 + 3 Combine like terms: -3.741657387 + 3 = -0.741657387 x2 = -0.741657387 Simplifying x2 = -0.741657387 Reorder the terms: 0.741657387 + x2 = -0.741657387 + 0.741657387 Combine like terms: -0.741657387 + 0.741657387 = 0.000000000 0.741657387 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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